It took some time but I think I've finally found a way to get improve NEDI enough to make it competitive with NNEDI3. It took a while since all algorithms related to NEDI (including aQua, SAI, and adaptations thereof) seem to suffer from the same flaw: there seems to be no way to get them simultaneously fast, numerically stable, and sharp (especially on vertical/horizontal edges).
So I needed to find a different approach. And I found one, in the article "Image Interpolation by Super-Resolution" by Alexey Lukin, Andrey S. Krylov, and Andrey Nasonov. The approach they took was to treat upscaling as a sort of inverse downscaling. They also show that this works nicely together with NEDI. From the kind of images I was able to create, using this approach, I'm also reasonably sure this was part of the inspiration behind the SmartEdge algorithm that Alexey Lukin showcases on
his website.
Anyway here is an example of the images I got using NEDI combined with the "SuperRes" method:
Castle (NEDI + SuperRes)
Castle (NNEDI3, 16 neurons)
Castle (NEDI)
Castle (Jinc3AR)
Lighthouse (NEDI+SuperRes)
Lighthouse (NNEDI3, 16 neurons)
Lighthouse (NEDI)
Lighthouse (Jinc3AR)
By the way, I think there's still room for improvement; the super-resolution method is incredibly flexible. Although, I think it will be difficult to find the right parameters by hand.